Question: Compute the expressions.
10. $(-4) + 2 = -4 + 2$
11. $(-4) - 2$
12. $(-4) - (-2)$
13. $30 - (-12)$
14. $(-32) - 62$
15. $-52 + 37$
16. $-(-37) - (+22)$
1. **Problem:** Compute $(-4) + 2$.
Formula: Addition of integers.
Work: $$-4 + 2 = -2$$
Explanation: Adding a positive number to a negative number moves the value towards zero.
2. **Problem:** Compute $(-4) - 2$.
Formula: Subtraction of integers.
Work: $$-4 - 2 = -4 + (-2) = -6$$
Explanation: Subtracting a positive number is the same as adding its negative.
3. **Problem:** Compute $(-4) - (-2)$.
Formula: Subtracting a negative number is adding the positive.
Work: $$-4 - (-2) = -4 + 2 = -2$$
Explanation: Two negatives make a positive in subtraction.
4. **Problem:** Compute $30 - (-12)$.
Formula: Subtracting a negative number is adding the positive.
Work: $$30 - (-12) = 30 + 12 = 42$$
Explanation: Subtracting a negative is like adding.
5. **Problem:** Compute $(-32) - 62$.
Formula: Subtracting a positive number from a negative number.
Work: $$-32 - 62 = -32 + (-62) = -94$$
Explanation: Subtracting a positive number moves further negative.
6. **Problem:** Compute $-52 + 37$.
Formula: Addition of integers.
Work: $$-52 + 37 = -15$$
Explanation: Adding a smaller positive number to a larger negative number moves towards zero.
7. **Problem:** Compute $-(-37) - (+22)$.
Formula: Double negative and subtraction.
Work: $$-(-37) - 22 = 37 - 22 = 15$$
Explanation: Negative of negative is positive; then subtract.
**Final answers:**
10. $-2$
11. $-6$
12. $-2$
13. $42$
14. $-94$
15. $-15$
16. $15$